A nitrogen-diluted hydrogen flame is modeled numerically in a plane two-dimensional counterflow configuration using a constant density, one-step reaction model and an optically thin radiation model. The 1D steady-state flame response shows duel extinction limits, namely the low Damkhler number (high stretch rate) blow-off extinction limit and the high Damkhler number (low stretch rate) radiative extinction limit. For high-stretch radiative flames there exist cellular flame structures close to and beyond the 1D blow-off extinction limit, thereby indicating the ability of flame to resist quenching by stretch. High-stretch flame results indicate that the 2D bifurcation from the one-dimensional flame response curve, previously reported for the adiabatic flames, exists for flames with radiative heat loss as well. Close to the 1D radiative extinction limit the 1D low-stretch radiative flame exhibits oscillatory response, indicating that oscillatory instability in diffusion flames can be triggered by radiative heat loss. The flame oscillation eventually leads to flame extinction at a stretch rate higher than the corresponding steady-state 1D radiative extinction limit, thereby demonstrating the ability of the low-stretch flames to resist quenching by radiative loss. Towards the low-stretch radiative extinction limit a similar bifurcation of the two-dimensional flame branch from the one-dimensional flame response curve is obtained. The dependences of the structure and transition of the two-dimensional cellular flames on the initial profile were studied on the bifurcated 2D branches obtained near the high-stretch and the low-stretch extinction limits. The results suggest that the 2D bifurcations can exist even without the flame having an edge, though the transition of the flame on the bifurcated 2D branches is different when an initial flame edge is present.
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